Question

I don't know how to solve equations like this

Answer 1

`(1)/(1+ \tan^(2)x ) + (1)/(1+ \cot^(2)x ) \\ = (1)/(\sec^(2)x) + (1)/(\csc^(2)x) \ \ \ \ \ \ \ [1+ \tan^(2)x = \sec^(2)x \ and \ 1+ \cot^(2)x = \csc^(2)x] \\ = (\csc^(2)x+\sec^(2)x)/((\sec^(2)x)(\csc^(2)x)) \\ = ( (1)/(\sin^(2)x)+ (1)/(\cos^(2)x))/( (1)/(\sin^(2)x)* (1)/(\cos^(2)x)) \\ = ( (\cos^(2)x+\sin^(2)x)/((\sin^(2)x)(\cos^(2)x)) )/( (1)/((\sin^(2)x)(\cos^(2)x))) \\ = \cos^(2)x+\sin^(2)x \\ =1`